In the triangle ABC AC = BC, the CH height is 26, cosA = √2 / 2. find AB
| March 16, 2021 | education
The AСН triangle is rectangular.
Determine the sine of the CAН angle. Sin2CAH = 1 – Cos2CAH = 1 – 1/2 = 1/2.
SinA = √2 / 2 = CH / AC.
AC = CH / (√2 / 2) = 26 / (√2 / 2) = 26 * √2 cm.
Then AH ^ 2 = AC ^ 2 – CH ^ 2 = 1352 – 676 = 676.
AH = 26 cm.
The height of CH is also its median of the triangle ABC, then AB = 2 * AH = 2 * 26 = 52 cm.
Answer: The length of the AB base is 52 cm.
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